Microscopic theory of capillary pressure hysteresis based on pore-space accessivity and radius-resolved saturation

Abstract

Continuum models of porous media use macroscopic parameters and state variables to capture essential features of pore-scale physics. We propose a macroscopic property "accessivity" (α) to characterize the network connectivity of different sized pores in a porous medium, and macroscopic state descriptors "radius-resolved saturations" (ψ w (F ), ψ n (F )) to characterize the distribution of fluid phases within. Small accessivity (α → 0) implies serial connections between different sized pores, while large accessivity (α → 1) corresponds to more parallel arrangements, as the classical capillary bundle model implicitly assumes. Based on these concepts, we develop a statistical theory for quasistatic immiscible drainage-imbibition in arbitrary cycles, and arrive at simple algebraic formulae for updating ψ n (F ) that naturally capture capillary pressure hysteresis, with α controlling the amount of hysteresis. These concepts may be used to interpret hysteretic data, upscale pore-scale observations, and formulate new constitutive laws by providing a simple conceptual framework for quantifying connectivity effects, and may have broader utility in continuum modeling of transport, reactions, and phase transformations in porous media.

Inferring pore connectivity from sorption hysteresis in multiscale porous media

“…Since connectivity plays a vital role in determining the transport properties of a material [89,90], it would be very interesting for future research to examine the relationship between f and z and the permeability to single-phase flow. More generally, for multiphase flow in porous media, this could lead to improved mathematical models of the relative permeability and capillary pressure [16], which also exhibit strong and poorly understood hysteresis.…”

“…In this article we are mainly concerned with the case where the solid matrix of the porous media is fully wetted by the adsorbate, thus minimizing the importance of contact angle hysteresis [12,13,14,15]. This mechanism is important in non-wetting solid-liquid contacts such as mercury porosimetry, though it still does not explain all the hysteresis in that case [12,16].…”

Freezing point depression and freeze-thaw damage by nanofluidic salt trapping

“…As shown in Fig. 1(a), even after partial freezing, an individual pore may remain open, allowing ions and water molecules to exchange freely with a reservoir of bulk solution via a percolating liquid path to neighboring unfrozen pores or an external bath [46][47][48][49][50]. In this scenario, the liquid electrolyte and any solid ice within the pore remain at quasiequilibrium with the bulk reservoir at a constant chemical potential.…”

“…Even if some solvated ions can diffuse through a given bottleneck, their electrokinetic transport rate may be too slow to allow many to escape prior to more complete freezing [51][52][53]. Such slow ion transport may be enhanced by long, tortuous pathways through a series of bottlenecks [54][55][56][57] and compounded by a large volume of micropores, effectively cut off from the macropores with insufficient time for salt release, in materials of low pore-space accessivity [50]. Even in relatively well-connected porous structures, nanofluidic salt trapping can also result from bottlenecks created by the advancing ice, as shown in Fig.…”

Impact of network heterogeneity on electrokinetic transport in porous media

“…The two types of networks correspond to different ranges of "accessivity", α, a recently proposed parameter that quantifies the degree of parallel versus series connectivity in a finite porous network. 53 The classical picture of a "capillary bundle" of parallel straight pores corresponds to the limit α = 1, since every pore is directly connected to the surface, like resistors in parallel. As we shall demonstrate, our hierarchical networks have intermediate accessivity, which is associated with greatly enhanced electrokinetic convection.…”